Non-linear vibration of variable speed rotating viscoelastic beams

Younesian, Davood; Esmailzadeh, Ebrahim

doi:10.1007/s11071-009-9589-6

Cited by 40 publications

(8 citation statements)

References 24 publications

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“…In addition, the early research that focused on the problem of rotating nonconstant speed was done in the work by Kammer and Schlack (1987). Nonlinear vibration of a variable speed rotating beam was studied by Younesian and Esmailzadeh (2010), where the influence of various parameters was investigated. The nonlinear dynamic response of a rotating blade with varying rotating speed was investigated by Yao et al (2012), and the results showed that the dynamic responses of the rotating blade changed from periodic motions to chaotic motions with different rotating speeds.…”

Section: Introductionmentioning

confidence: 99%

Dynamic and resonance response analysis for a turbine blade with varying rotating speed

Wang

Hao

Chen

et al. 2018

jtam

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A coupling model between turbine blades with a varying rotating speed and oncoming vortices is constructed, where the coupling of the structure and the fluid is simulated by the van der Pol oscillation. Partial differential governing equations of motions for the coupled system are obtained and discretized by using the Galerkin method. The 1:2 subharmonic resonance and the 1:1 internal resonance are investigated with the multiple scale method and first-order averaged equations are then derived. Nonlinear responses and bifurcation characteristics are studied by a numerical integration method. Stability of bifurcation curves is determined by utilizing the Routh-Hurwitz criterion. The effect of system parameters including the detuning parameter, steady-state rotating speed, amplitude of periodic perturbation for the rotating speed and freestream velocity on vibration responses are investigated.

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Section: Introductionmentioning

confidence: 99%

Dynamic and resonance response analysis for a turbine blade with varying rotating speed

Wang

Hao

Chen

et al. 2018

jtam

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“…The linear natural frequencies of beams that rotate with constant speed were investigated by many researchers, for example in [1][2][3][4][5]. Works that consider geometrically nonlinear models of rotating beams may be found, for example [6][7][8]. In what concerns modern wind turbine blades, most of them are constructed with load carrying box girder inside the blade and shells on the surface of the blade [9].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Stoykov¹,

Margenov²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The geometrically nonlinear vibrations of 3D beams that rotate about a fixed axis are investigated by the p-version finite element method. The beams are considered to be tapered, i.e. with variable thickness along its length, and with arbitrary cross sections. The beam model is based on INTRODUCTIONRotating beams are used to model and investigate the dynamics of helicopter blades, jet engine turbine blades, robot arms, wind turbine blades, etc. Many studies have been performed for modeling rotating beams about a fixed axis. The linear natural frequencies of beams that rotate with constant speed were investigated by many researchers, for example in [1][2][3][4][5]. Works that consider geometrically nonlinear models of rotating beams may be found, for example [6][7][8]. In what concerns modern wind turbine blades, most of them are constructed with load carrying box girder inside the blade and shells on the surface of the blade [9]. The purpose of the box girder is to make the blade stronger and stiffer while the shells around the box girder form the aerodynamic shape. Thus, the dynamic behavior of the wind turbine blade might be determined mainly from the load carrying box, even though the shells contribute small bending strength.In the current work, a model of beams rotating about a fixed axis with constant speed of rotation is presented. A setting angle and a rigid hub are included in the model. The equation of motion is derived in the rotating coordinate system, and the rotation is taken into account by the inertia forces [10]. The beam may vibrate in space, i.e. it may perform longitudinal, torsional and bending deformations, the model is based on Timoshenko's theory for bending and assumes that under torsion, the cross section deforms only in longitudinal direction due to warping [11]. Geometrical type of nonlinearity is considered and the equation of motion is derived by the principle of virtual work.Thin-walled box beams with linearly varying thickness and width are investigated. First, the derived model is validated by generating a fine mesh of three-dimensional finite elements. Then, the influence of the setting angle and the speed of rotation on the natural frequencies is examined. Forced vibrations of rotating beams due to harmonic forces are presented.

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“…Dasa et al [14] investigated the free out-of-plane vibration of a rotating beam with a non-linear spring mass system using a perturbation method. The non-linear coupled longitudinal and bending vibration of a variable speed rotating beam was modelled by Younesian and Esmailzadeh [15]. The solution of the nonlinear partial differential equation of motion was assumed to be a series of multiplications of time and position functions in accordance with the Galerkin modal summation technique.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

Esfandiar¹,

Daneshmand²

2013

sajie

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In this paper, based on the Voigt-Kelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the model's dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamilton's principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude. OPSOMMING'n Voigt-Kelvin saamgestelde model word in 'n nie-reglynige dinamiese oplossingsruimte gebruik om 'n soepel hanteringsrobot te ontleed. Die modellering is daartoe instaat om nielinêre dinamiese vertoning van styfheid wat ontstaan wees sentrifugale en Corioliskragte te ontleed. Die modelvergelykings is gebaseer op die Hamiltonbeginsel. Simulasieresultate toon betekenisvolle verbetering van sisteemgedrag. Verdere ontledings handel oor strukturele demping en vibrasie-amplitude.

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Non-linear vibration of variable speed rotating viscoelastic beams

Cited by 40 publications

References 24 publications

Dynamic and resonance response analysis for a turbine blade with varying rotating speed

Dynamic and resonance response analysis for a turbine blade with varying rotating speed

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

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